⊥+∑📈⇒✨∞=1️⃣

#borel-cantelli #second borel-cantelli #probability theory #sum of probabilities #infinitely often #almost surely #limsup events

∑📉⇒✨∞=0️⃣

#borel-cantelli #first borel-cantelli #probability theory #sum of probabilities #infinitely often #almost surely #limsup events

ℛAₙ)∈{0️⃣1️⃣}

#borel-cantelli #measure theory #zero-one law #limsup measure #probability space #infinite events

∑=∞+🎲↔️🎲⇒P(🎯∞)=1

#borel-cantelli #probability sum divergence #infinitely many events #independent events #measure theory #converse borel-cantelli

∑<∞⇒P(🎯∞)=0

#borel-cantelli #probability sum convergence #finitely many events #measure theory #sequence of events